Jed Rothwell wrote:
Here is the antidote to the nonsense published here and elsewhere by
conspiracy theorists:
http://wtc.nist.gov/pubs/factsheets/faqs_8_2006.htm
Example:
"As documented in Section 6.14.4 of NIST NCSTAR 1, these collapse times
show that:
“… the structure below the level of collapse initiation offered minimal
resistance to the falling building mass at and above the impact zone.
The potential energy released by the downward movement of the large
building mass far exceeded the capacity of the intact structure below to
absorb that energy through energy of deformation.
Since the stories below the level of collapse initiation provided little
resistance to the tremendous energy released by the falling building
mass, the building section above came down essentially in free fall, as
seen in videos. As the stories below sequentially failed, the falling
mass increased, further increasing the demand on the floors below, which
were unable to arrest the moving mass.”
In other words, the momentum (which equals mass times velocity) of the
12 to 28 stories (WTC 1 and WTC 2, respectively) falling on the
supporting structure below (which was designed to support only the
static weight of the floors above and not any dynamic effects due to the
downward momentum) so greatly exceeded the strength capacity of the
structure below that it (the structure below) was unable to stop or even
to slow the falling mass.
Obviously this not exactly correct as written -- an impact with a
stationary mass must slow a moving mass, simply by conservation of
momentum. However, it's worth taking a moment to consider something
I've seen several people say, in this group and elsewhere: "If each
floor had delayed the fall by only one second, then..."
Simple physics says each floor wouldn't delay the fall by anywhere near
one second.
The floors are something like 18 feet apart, yes? Time to free-fall 18
feet is roughly 1 second. But after 1 second, the freefalling object is
moving at about 32 feet/second.
Impact on the floor below travels through the structure at the speed of
sound, which we can take to be infinite for this analysis, since it
requires only a tiny fraction of a second for the shock to get to all
support points of the newly impacted floor. Either the supports break
(essentially instantly) or they don't. If they don't, then the fall is
arrested, and the collapse stops right there. If they do, they break at
the moment of maximum stress, which, again, is when the first, largest
shock wave gets to them, which is essentially at the moment of impact.
So the combined mass continues on its way almost immediately, but now
it's only moving at 16 feet/second, because it has the same momentum but
double the mass. We would like to know how long the combined mass will
take to fall another 18 feet; with an initial velocity of v0, and
acceleration of "g", and a distance to fall of X feet, I make it about
dt = [-v0 + sqrt(v0^2 + 2gX)]/g
(where I took the positive square root for reasons of realism).
Plugging this into a spreadsheet, the time for the combined mass to
traverse the next 18 feet will be 0.66 seconds, versus 0.44 seconds if
it feel freely: the delay is about 0.22 seconds.
The delay due to striking the third floor and bringing it up to speed
will be about 0.11 seconds -- just half the delay due to the impact with
the second floor. With each successive floor, the effect of adding a
another floor to the "package" becomes smaller, and the total reduction
below free-fall speed is clearly going to be a whole lot smaller than
the result of the naive speculation, "Suppose the mass hesitated for a
second at each floor...".
I haven't pushed this crude back-of-the-envelope calculation through to
see how well it agrees with the actual reported speed of descent but
looking at the results of the first three floors, and realizing that, as
the falling mass increases, the effect of each succeeding floor _must_
become rapidly smaller, an observed fall speed which was nearly equal to
free-fall doesn't sound unreasonable.
The downward momentum felt by each successive
lower floor was even larger due to the increasing mass."
- Jed
